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def definition def or abbrev

SchlaefliRowSum

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 311def SchlaefliRowSum {n : ℕ} (W : WeakFieldReggeData n) : Prop :=

proof body

Definition body.

 312  ∀ i : Fin n, ∑ j : Fin n, bilinearCoefficient W i j = 0
 313
 314/-- The second-order Regge action functional in the conformal mode.
 315    Plugging the conformal expansion of `ℓ²` into the linearized Regge
 316    action and collecting the order-`ξ²` terms gives this bilinear:
 317
 318        S^(2)[ξ] = (1/4) · Σ_{i,j} (ξ_i + ξ_j)² · M_{ij}
 319                = (1/4) · Σ_{i,j} (ξ_i² + 2 ξ_i ξ_j + ξ_j²) · M_{ij}.
 320
 321    The factor `1/4` comes from the `(ξ_i + ξ_j)/2` factors entering
 322    twice (once from `A_h^(1)`, once from `δ_h^(1)`).
 323
 324    With the Schläfli row-sum property, the `ξ_i² + ξ_j²` parts
 325    vanish on summation and the `2 ξ_i ξ_j` part rearranges via §2 into
 326    the Dirichlet form on differences. -/

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